(°ru tcb*A-  &■  f drajuo- 


of  the  American  Institute  of  Electrical  Engin- 
eers , Buffalo , August  22nd , iqoi . 


[advance  copy  subject  to  revision] 
POWER  FACTOR  INDICATORS. 


BY  WILLIAM  HAND  BROWNE,  JR. 


The  introduction  of  induction  motors  in  factories  brings  with 


it  a power  factor  considerably  less  than  unity.  Since  this  re- 
quires a larger  current  for  a given  power  delivered,  the  total 
available  output  of  the  generating  plant  is  less,  and  the  efficiency 
of  the  system  is  lower  than  if  the  load  were  non-inductive.  Fui- 
ther,  the  wattless  component  of  the  current  causes  increased 
armature  reactions,  and  consequently  seriously  affects  the  regula- 
tion of  the  system. 

It  therefore  may  be  thought  desirable  to  balance  wholly  or  in 
part  the  wattless  component  of  current,  due  to  the  induction 
motors,  by  the  use  of  synchronous  motors  or  converters,  and  it 
then  becomes  necessary  to  have  some  means  of  knowing  when 
this  has  been  accomplished. 

Methods  of  Determining  Balance. — One  method  of  judging 
the  conditions  of  the  system,  which  is  used  to  some  extent,  is  to 
place  an  ammeter  in  the  line  carrying  the  current  for  both  in- 
duction and  synchronous  motors.  Then  to  secure  a balance,  the 
excitation  of  the  synchronous  motor  is  changed  until  the  line  cur- 
rent is  a minimum.  This  method,  while  simple,  is  exceedingly 
crude,  and  becomes  entirely  unreliable  when  the  synchronous 
motor  is  fairly  well  loaded.  As  the  power  factor  of  the  system 
approaches  unity  under  these  conditions,  a comparatively  large 
change  in  the  excitation  of  the  synchronous  motor  produces  little 
or  no  apparent  change  in  the  ammeter  reading.  This  is  because 
the  characteristic  v curve  of  the  synchronous  motor,  i.  e .,  arma- 


475 


476 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


ture  current  on  a field  current  base,  is  quite  flat  for  large  loads. 
The  wattless  component  of  current,  however,  changes  very  rapidly 
as  will  be  shown  later.  The  same  criticism  applies  to  the  use  of 
an  indicating  wattmeter  for  securing  balance.  Here  the  excita- 
tion of  the  synchronous  motor  is  changed  until  the  volt  amperes 
as  found  from  the  ammeter  and  voltmeter  readings  are  equal  to 
the  true  watts  as  indicated  by  the  wattmeter. 

To  show  that  both  of  these  methods  are  unreliable,  suppose  a 
small  error  has  been  made  in  reading  the  ammeter  or  wattmeter, 
due  to  carelessness  or  to  instrumental  errors.  Fig.  1 illustrates  the 
effect  of  this  error  on  the  wattless  component  of  current,  or  what 


Fig.  1. — Curve  showing  the  rate  of  change  of  the  sine  with  the  cosine. 


is  the  same  thing  on  sin  the  inductance  factor  ; k l represents 
the  power  factor  for  different  percentage  differences  between  the 
true  and  apparent  watts,  m n is  the  corresponding  inductance  factor 
curve.  For  an  error  of  1 per  cent,  the  inductance  factor  is  .14. 
For  an  error  of  2 per  cent,  the  wattless  component  of  current  is 
nearly  20  per  cent,  of  the  total  current.  That  is  to  say,  when  the 
attendant  thinks  he  has  secured  a balance,  the  wattless  current  fnay 
still  be  a very  considerable  fraction  of  the  whole,  and  seriously 
affect  the  regulation  of  the  generator. 

Behavior  of  a Synchronous  Motor.— Fig.  2 shows  how  a syn- 
chronous motor  will  behave  under  these  conditions.  Here  a con- 


1901. J BROWNE  ON  POWER  FACTOR  INDICATORS.  477 

Btant  applied  voltage  and  a constant  true  watts  input  have  been 
assumed,  with  a variable  inductance  factor.  That  is  to  say, 
El  cos  (p  is  constant,  at  5 kilowatts,  represented  by  the  horizontal 
line  fa.  (Fig.  2). 

The  base  taken  here  is  El  sin  <p.  The  curve  b c is  cos  <p  for  diff- 
erent values  of  El  sin  ip.  The  curve  o d shows  the  corresponding 
values  of  sin  ip  ; f q is  the  armature  current.  These  curves  show 


that  as  we  approach  unity  power  factor  cos  ip  changes  slowly  and 
the  total  current  changes  slowly,  but  sin  ip  (and  hence  / sin  ip) 
changes  very  rapidly. 

The  need  of  an  instrument  which  will  indicate  accurately  the 
condition  of  the  system  as  regards  balance  being  evident,  it  be- 
comes worth  while  examining  the  methods  and  instruments 
available  for  such  determinations,  as  well  as  the  quantities  to  be 
measured.  The  phase  difference  of  two  waves  is  usually  defined 
as  the  displacement  in  degrees  between  the  points  where  they 


478 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


pass,  in  the  same  direction,  through  zero  or  their  maximum 
values.  In  alternating  current  theory,  where  the  two  waves  are 
assumed  sinusoids  and  one  is  the  e.m.f.  and  the  other  the  cur- 
rent, the  cosine  of  the  phase  angle  is  called  the  power  factor.  It 
is  equal  to  the  ratio  of  true  watts  to  volt  amperes.  In  practice 
while  we  may  not  have  sinusoids,  this  ratio  is  still  called  the 
power  factor  and  may  be  considered  as  the  cosine  of  the  phase 
angle  of  the  equivalent  sinusoids. 

As  pointed  out  above,  measurements  for  determining  the  phase 
angle  are  unsatisfactory  when  involving  the  cosine,  if  the  cosine 
approaches  unity.  We  must  measure  either  the  phase  angle 
directly  or  indirectly,  or  what  in  most  cases  would  be  equally 
satisfactory,  the  wattless  volt  amperes ; that  quantity  Mr.  Stein- 
metz  has  called  the  “ wattless  power.” 

Unfortunately  few  of  the  methods  suggested  for  measuring 
these  quantities  are  more  than  laboratory  methods,  and  the  in- 
struments used  are  unsuitable  for  practical  work.  The  split 
dynamometer  of  Blakesley,  the  three  voltmeter  method  of  Flem- 
ing, and  the  three  ammeter  method  of  Sumpner  are  too  familiar 
to  need  description  here,  and  are  hardly  applicable  under  the 
usual  operating  conditions.  There  are,  however,  two  or  three 
instruments  which  give  satisfactory  gervice  under  proper  con- 
ditions. 

Glassification.. — Power  factor  indicators  may  be  divided  into 
four  classes : 

1.  Phase  meters,  by  which  the  phase  angle  is  determined 
directly. 

2.  Power  factor  meters,  measuring  a function  of  the  phase 
angle. 

3 Wattless  power  meters,  measuring  El  sin  ip. 

A.  Wattless  current  meters,  measuring  1 sin  ip. 

In  the  first  class  we  may  include,  in  addition  to  types  to  be 
described  below,  all  forms  of  oscillographs  and  curve  tracers. 

In  the  second  class  we  may  include  all  instruments  measuring 
sin  ^.and  tan  (p  as  well  as  cos  ip. 

These  classes  may  be  further  subdivided,  according  to  the 
means  employed  to  obtain  an  indication,  into  four  types : 

(a.)  Electromagnetic,  using  the  force  of  attraction  of  electro- 
magnets. 

(i b .)  Electro-dynamic,  utilizing  the  reaction  between  coils  carry- 
ing currents. 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


47& 


( c .)  Induction,  a rotating  magnetic  field  is  set  up  and  used  to 
deflect  a disk. 

( d ) Electrolytic,  depending  upon  electrolysis  to  secure  a 
record. 

Phase  Meters. — The  various  types  of  oscillographs  and  curve 
tracers  are  too  well  known  to  need  description.  In  general  they 
are  laboratory  instruments  and  not  applicable  to  commercial 
working. 

Tumtfs  Phase  Meter 1 (1&).— Let  the  pair  of  coils  a b (Fig.  3) 
carry  the  current  whose  phase  angle,  referred  to  the  e.  m.  f.  is 
desired. 

Within  the  space  between  the  two,  suspended  freely,  is  the 
movable  system  c d,  consisting  of  two  independent  windings  con- 
nected together  mechanically  at  right  angles.  Let  a be  the  angle 


which  d makes  with  the  axis  of  a b. 

When  a current  ix  — lx  sin  (co  t — <p ) passes  through  a b;  this 
sets  up  an  alternating  flux  in  the  space  between  them  equal  to 

N = sin  (co  t — <p) 

JV0  being  the  maximum  value  of  the  flux  and  co  times  the  fre- 
quency. Through  d pass  a current  in  phase  with  the  e.  m.  f. 
This  will  be 

i.z  = f2  sin  co  t 


1.  J.  Tuma  in  Sitzungsberichte  der  K.  Preussischen  Akademie  dev  Wissen- 
schaften,  vol.  106,  p.  521,  1897.  M.  Brieger  in  Bulletin  de  V Association  des 
Ingenieurs  Elcctriciens,  vol.  11,  p.  79,  1899.  Aug.  J.  Bowie,  Jr.,  in  Electri- 
cal World  a.nd  Engineer,  vol.  86,  p.  644,  1900.  (Mr.  Bowie  works  out  the  gen- 
eral condition  and  shows  the  application  to  two  and  three-phase  circuits.)  H. 
Armangat  in  L Eclair  age  Electriqne , vol.  25,  p.  339.  (Hartmann  and  Braun 
instrument.) 


480 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


And  through  c pass  a current  in  quadrature  with  this 
h = h sin  (co  t — ^ 

The  torque  set  up  between  a b and  d will  be 

Tx  — N i2  sin  a 

Between  a b and  c 

T2  = N % cos  a 

Substituting  for  n,  i2  and  i3,  the  values  given  above,  the  effec- 
tive values  are 

rji  jVq  L • 

1 1 = — - — * sin  a cos  (p 
2 y 


T — ^ ) 


cos  a sin  (p 


Since  the  coil  is  free  to  turn,  the  angle  a will  be  such  that 
Tx  = T2 , then 


#0 


sin  a cos  (p 


nqi2 


cos  a sin  (p 


tan  a ::  tan  ip 

The  angle  a is  the  phase  angle. 

Induction  Phase  Meters  (Id). — If  we  pass  through  two  coils, 
concentric  but  set  at  an  angle  with  each  other,  currents  which 
set  up  equal  fluxes  differing,  however,  in  phase,  a rotating  mag- 
netic field  of  elliptical  form  will  in  general  be  created.  If  the 
two  coils  are  inclined  at  an  angle  which  is  the  supplement  of  the 
phase  angle,  the  resulting  field  will  have  a constant  value.  An 
armature  suitably  placed  in  such  a field  will  cause  a ray  of  light 
reflected  from  an  attached  mirror  to  travel  in  a circle.  In  apply- 
ing this  method  it  is  necessary  to  have  the  fluxes  of  equal  value 
and  to  change  the  angle  between  the  coils  until  the  ellipse  be- 
comes a circle  when  the  phase  angle  is  read  off  directly.  The 
instruments  of  Angelmeyer1 2,  Korda1,  Hess1,  Rossi3  and  one  of 
Arno3,  make  use  of  this  principle. 

1.  (a)  “Mesure  des  Differences  de  Phase.”  P.  Fontaine  in  Bulletin  de  V As- 
sociation des  Ingenieurs  Electriciens , Nov.  1899. 

2.  L'Edairage  Electrique,  vol  15,  pp.  133,  322,  355,  1898. 

3.  Ibid , vol.  21,  p.  225,  1899. 


1901.]  BROWNE  ON  POWER  FACTOR  INDICATORS . 


481 


Electrolytic  Phase  Indicator  (16?.) — A very  simple  device,  due 
to  Janet1,  consists  of  a metallic  drum  upon  which  rest  two  styli 
of  iron.  One  of  these  is  connected  so  as  to  have  a difference  of 
potential  between  it  and  the  drum  which  is  in  phase  with  the 
current,  the  other  one  which  is  in  phase  with  the  e.  m.  f.  On 
the  drum  is  stretched  a sheet  of  paper  which  has  been  soaked  in 
potassium  ferrocyanide  and  ammonium  acetate. 

When  the  difference  of  potential  between  either  stylus  and  the 
drum  reaches  a certain  positive  value,  electrolysis  begins  and  the 
paper  under  that  stylus  turns  blue.  Now  if  the  drum  be  turned, 
each  stylus  traces  a broken  blue  line  on  the  paper,  each  blue 
mark  representing  part  of  a positive  half  wave.  The  angular  dis- 
tance from  the  center  of  one  of  these  short  lines  and  that  of  the 
corresponding  mark  made  by  the  other  stylus,  expressed  in  elec- 
trical degrees,  is  the  phase  angle.  This  is  true  only  when  the 
two  waves  have  the  same  form. 

Power  Factor  Meters  (2). — Two  harmonic  motions  acting  at 
right  angles  and  having  the  same  frequency  and  amplitude  but  a 
difference  in  phase  of  90°,  will  produce,  if  acting  at  the  same 
time,  a uniform  circular  motion.  If  the  amplitudes  are  not  the 
same,  the  result  is  an  ellipse,  the  major  and  minor  axes  of  which 
are  the  respective  paths  of  the  two  harmonic  motions. 

If  the  phase  difference  is  not  90°  the  two  axes  of  the  resulting 
ellipse  do  not  coincide  in  direction  with  the  two  harmonic  mo- 
tions. 

Puluy's  Power  Factor  Meter  (2a). — The  principle  just  de- 
scribed has  been  made  use  of  by  Puluy.  Two  electro-magnets, 
through  the  winding  of  each  of  which,  one  of  the  currents,  the 
phase  difference  of  which  is  desired,  is  passed,  act  upon  two  ar- 
matures causing  them  to  vibrate  in  planes  normal  to  each  other. 
A ray  of  light  falling  upon  a mirror  attached  to  one  of  these  and 
reflected  to  a second  mirror  on  the  other,  and  thence  to  a screen, 
will  describe  an  ellipse,  the  shape  and  position  of  which  is  de- 
termined by  the  values  of  the  two  currents  and  the  phase  differ- 
ence. 

Let  X be  the  amplitude  of  one  vibration  and  Y that  of  the 
other.  It  is  evident  that  a rectangle,  the  sides  of  which  are  re- 
spectively 2 X and  2 Y,  can  be  circumscribed  about  this  ellipse, 
Fig.  4.  Now  when  either  one  of  the  magnets  is  acting  alone,  a 


1.  See  reference  ( a ) above. 


482 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


straight  line  will  be  described,  2 X or- 2 Y in  length.  The  inter- 
section of  these  lines  will  be  the  center  of  the  ellipse. 

The  co-ordinates  of  any  point  on  the  ellipse,  referred  to^  these 
two  lines,  will  be 

x = X sin  to  t (1) 

y — Y sin  {to  t — <p)  (2) 

tp  being  the  difference  in  phase 
In  equation  (1)  let  x = 0,  then 

to  t — n n 

n being  some  whole  number. 

Substituting  in  (2) 

Vo  = Y sin  (n  it  — tp) 

= ± Y sin  tp  = OC  (Fig.  4)  (3) 

Again  let  y = 0 in  (2),  then 

to  t — tp  = n 7i 
x0  = X sin  {n  tt  -)-  <p) 

— ± X sin  tp  — 0 D ^Fig.  4)  0 v(4) 
From  (3)  and  (4)  it  follows  that 


sin  tp 


o c _ o_d 

O B ' 0~A 


MorlancPs  Power  Factor  Meter. — In  an  apparatus  described 
by  Mr.  Morland1,  the  two  conductors  carrying  the  two  currents 
pass  between  the  poles  of  a permanent  magnet.  Each  of  these 
causes  a small  mirror  to  vibrate,  producing  the  result  just  des- 
cribed. 

Claude's  Power  Factor  Meter. — Claude2  places  the  two  elec- 
tro-magnets in  direct  opposition  and  causes  them  to  actuate  the 
same  armature.  Let  the  maximum  flux  set  up  by  each  coil  be  N. 
The  ray  of  light  reflected  from  the  mirror  will  under  the  influ- 
ence of  the  flux  X oscillate  along  a path  in  length  K X,  K being 
a constant.  If  both  coils  were  acting  and  if  the  currents  were  in 
phase,  the  length  of  this  path  would  be  2 K X. 


1.  Apparatus  for  illustrating  change  of  phase,  S.  I.  Moreland,  Electrical  En- 
gineer, Vol.  28,  p.  237.  Sept.  8,  1898. 

2.  See  reference  ( a ) above. 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


483 


Call  this  dx.  At  any  instant  the  flux  due  to  one  coil  will  be 


JVt  = N sin  (o  t 

(1) 

That  due  to  the  other  will  be 

N2  = N sin  (a)  t — (f) 

(2) 

Writing  (1) 

f 

+ 

I 

3 

*QQ 

tei 

II 

and  (2) 

N%  = N sill  [(cot  — I]  — 1 1 

L\  -A  2 J 

and  taking  the  sum  we  have 

N,  + = 2N  sin  (co  t — cos  | 


and  the  path  to  the  ray  is 


Call  this  d2. 

Then  it  follows  that 


2 N K cos  2. 

2 


It  is  evident  from  what  has  been  said  above  that  this  method 
will  not  be  accurate  when  <p  approaches  zero. 

Rayleighs  Power  Factor  Meter  (2a). — Lord  Rayleigh’s  ap- 
paratus1 for  measuring  phase  angles  is  somewhat  similar  to  the 
above.  The  movable  loop  is  replaced  by  a soft  iron  needle  and 
the  two  coils  are  placed  on  opposite  sides  of  this.  The  equation 
then  becomes 

+ ^2  + 2 \/dtd2  cos  <p  = ds 

The  deflections  are  measured  as  in  a reflecting  galvanometer. 
Mr.  Edwin  Place2  gives  the  results  of  a great  number  of  experi- 
ments made  with  an  instrument  of  this  type.  He  shows  that  the 
angle  found  in  this  way  is  that  between  the  equivalent  sine  waves. 
The  cosine  of  this  angle,  however,  is  not  given  by  the  ratio  of 
true  watts  to  volt  amperes,  the  true  power  factor. 

Tuma3  describes  an  instrument  similar  to  the  above  but  with 


1.  Philosophical  Magazine,  May,  1897. 

2 Electrical  World  and  Engineer , May  13,  1899.  p.  614. 

3.  Sitz u n guberichte  der  K.  Preussischen  Akademie  der  Wi  sens  haf ten  (Berlin) 
vol.  106,  p.  442,  1897. 


484 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


the  coils  at  right  angles.  One  of  these  lies  in  the  magnetic 
meridian. 

He  shows  that,  with  specially  wound  coils,  if  ip  is  the  phase 
angle  and  ip  the  angle  between  the  needle  and  that  coil  which 
lies  in  the  magnetic  meridian,  then 

cos  ip  = tan  2 p. 

Dynamometer  Types. — A Siemens  electro-dynamometer1  hav- 
ing two  fixed  coils  may  be  used  for  phase  angle  measurements 
if  the  movable  system  be  replaced  by  a coil  closed  upon  itself 
and  suspended  in  the  plane  of  the  other  two. 

1.  If  a current  ix  — Ix  sin  to  t be  passed  through  one  coil, 

it  will  set  up  an  e.  m.  f.  in  the  movable  loop 

ex  — — M a)  1 \ cos  io't. 

2.  When  the  current  i2  = 12  sin  (to  t — ip)  passes  through 

the  second  coil  it  will  set  up  in  the  movable  coil  an  e.  m.  f. 

e2  — — M o)  /2  cos  (to  t — ip) 

M is  the  mutual  inductance  and  is  assumed  the  same  in  each 
case. 

3.  If  the  two  currents  are  flowing  at  the  same  time,  we  have 
in  the  movable  coil 

e\  + e2  — — il/  co  [/j  cos  it)  t -|-  I2  cos  {to  — ip) J 

Denoting  the  angles  of  torsion  necessary  to  keep  the  mova- 
able  coil  in  its  zero  position  in  the  three  cases  by  dh  d2  and 
<#3,  respectively,  and  by  t the  constant  of  the  instrument  by  K, 
we  have 

Kdx  = M2  to2 1'\  efl 

Kd2  = M2  to2  722eff. 

jK  dz=  M2  (O2  (Kl\  efl  -f-  1\  eff  — 2 I\  1%  eff.  COS  ip) 

Hence 

d\-\-  d2  — 2 s/ dx  cos  <p  = ds 

and  the  phase  angle  is  deduced  from  this  relation. 


. See  reference  (a)  above. 


1901.]  BROWNE  ON  POWER  FACTOR  INDICATORS . 


485 


Arno’s  “ Tangent  Phase  Meter ” (2 b). — A second  power  meter 
of  Arno’s1  consists  of  a Siemens  electro-dynamometer  with  an 
additional  pair  of  coils  closed  upon  themselves  and  fastened  to- 
gether at  right  angles.  The  pair  as  a whole  is  suspended  within 
the  two  other  coils  and  may  be  held  in  any  position  by  a torsion 
spring.  In  Fig.  5 let  a and  b be  the  two  coils  of  the  dynamom- 
eter and  c and  d the  pair  of  short-circuited  loops. 

Passing  the  two  currents  through  a and  b respectively,  the  in- 
strument becomes  a wattmeter  and  we  have 

lx  /2  cos  cp  = ici  dx  (1) 


where  dx  is  the  angle  of  torsion  required  to  keep  the  movable 
coil  in  position.  hx  is  the  constant  for  this  system. 

Now  fix  b and  pass  the  current  Ix  through  a,  this  will  set  up 
in  c an  e.  m.  f. 


M Lx  CO  cos  CO  t 


M lx  co  sin 


(" 


This  will  cause  in  c a current 

ix  = — Ix  co  sin  (cot  — 

rx  . . 1 V 2/ 


1.  L’  Eclair  age  Electrique,  vol.  12,  p.  5.J0;  vol.  21,  p.  226;  vo],  25,  p.  484; 
also  reference  (a)  above. 


486 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


The  inductance  of  the  loop  is  assumed  negligible ; rx  is  the  re- 
sistance. 

This  current  being  in  quadrature  with  that  in  a will  set  up  no 
torque. 

The  current  in  a will  have  no  inductive  effect  upon  the  loop  n 
since  they  are  kept  at  right  angles. 

If  at  the  same  instant  a current  I2  is  passed  through  b,  we  will 
have  at  this  instant  in  b > 


h 


12  sin  (co  t — cp ) 


e2  = M /2  a)  sin  (co  t — - — cp) 


and  a current 


M T . , . 7T 
— 12  co  sin  (co  t — - 
r 2 


— 9) 


This  assumes  the  same  mutual  inductance  for  each  pair  of  coils 
and  the  same  resistance  for  the  two  loops  c and  d. 

This  current  will  react  with  that  in  a and  set  up  a torque  pro- 
portional to  their  product 

^ ^ I*  co  sin  co  t sin  (co  t — - — cp) 
v 2 

The  effective  value  of  this  torque  is 


M l,  I2 
2 r 


co  cos 


2 r 


co  sin  cp 


It  is  evident  that  the  couple  existing  between  b and  c will  have 
the  same  value  but  have  an  opposite  sign,  since  the  current  in  c 
being  in  quadrature  with  that  in  a will  be  less  than  90°  behind 
b,  while  that  in  d will  be  more  than  90°  behind  a. 

The  resulting  torque  of  the  system  is  proportional  to  Ix  I2  sin  cp 
and  may  be  written 

Ix  12  sin  = Jc2  d2  (2) 


where  k2  is  a constant  and  d2  the  angle  of  torsion. 


Dividing  (2)  by  (1)  we  have 


h d2 


= tan  cp 


giving  the  phase  angle  in  terms  of  its  tangent. 


1901.]  BROWNE  ON  POWER  FACTOR  INDICATORS.  487 

Breitfield's  Method  (2b). — Mr.  C.  Breitfield1  has  suggested  an 
application  of  an  ordinary  wattmeter  for  measuring  the  power 
factor  of  a three-phase  system.  The  current  coil  is  placed  in  one 
line  and  one  end  of  the  pressure  coil  also  connected  to  this  line. 
The  other  end  is  first  connected  to  the  second  line  and  then  to 
the  third.  In  the  first  case  we  have  the  deflection 

dx  = El  cos  (<p  — 30°) 

In  the  second 


d%  = E I cos  (<p  -|-  30°) 

From  these  equations  we  have 

d\  — d2  = E I sin  <p  sin  30° 


Hence 


di  + d2  = E I cos  <p  cos  30° 


tan  <p 


VS 


d\  — d* 
—d\  + d^ 


General  Electric  Company's  Instrument  (2b). — The  well- 
known  fact  that  the  ratio  of  the  readings  of  the  two  wattmeters 
used  to  measure  the  power  of  a three-phase  system  changes  with 
the  power  factor  and  is  unity  when  the  power  factor  is  unity,  has 
been  made  use  of  by  the  General  Flectric  Company  to  indicate 
the  power  factor.  The  instrument2  is  simply  two  wattmeters  of 
the  dynamometer  type,  the  movable  coils  of  which  are  attached 
to  the  same  spindle.  The  instrument  deflects  to  the  right  or  left 
according  as  the  current  lags  or  leads,  and  stands  at  zero  when 
the  system  is  balanced  and  the  power  factor  unity. 

Eerraris ’ Power  Factor  Meter  (2c.). — Ferraris3  combines  two 
harmonic  fields,  producing  a rotating  field  of  elliptical  form. 
Within  this  field  is  suspended  a short-circuited  coil  which  can  be 
held  in  any  position,  by  a torsion  spring,  as  is  the  movable  coil  of 
a Siemens  dynamometer.  The  force  required  and  therefore  the 
angle  through  which  the  spring  must  be  turned,  to  hold  the  coil 
in  any  position  is  proportional  to  the  square  of  the  intensity  of 
the  flux  in  that  direction.  Points  can  thus  be  determined  and 


1.  Electrotechnische  Zeitschrift,  vol.  20,  p.  120,  1899. 

2.  Electrical  World  and  Engineer , vol.  67,  p.  688,  April  27,  1901 . 

3.  See  reference  (a)  above. 


488 


BRO  WISE  ON  PO  WER  FA  GTOR  INDIG  A TORS.  [Aug.  22, 


the  ellipse  plotted  and  the  sine  of  the  phase  angle  deduced  as 
above.  (See  Puluy’s  Method,  page  481.) 

Power  Factor  Indicators  (3).  — In  the  methods  described 
above,  the  object  sought  was  the  determination  of  the  phase  angle. 
But  few  of  these  are  applicable  under  the  usual  operating  condi- 
tions. We  might  mention  as  useful  forms,  those  of  Turaa  and 
the  General  Electric  Co.  In  most  cases,  however,  we  are  more 
concerned  with  the  magnitude  of  the  wattless  component  of  cur- 
rent than  with  the  power  factor.  We  care  less  about  the  decrease 
in  the  total  output  than  about  the  poor  regulation  caused  by  in- 
ductive loads.  Instruments  which  will  indicate  the  wattless 
current,  or  rather  the  wattless  volt  amperes  are  easily  made  in 
commercial  form. 

“ Wattless  Wattmeters .”  Dynamometer  Type  (3b). — A Sie- 
mens dynamometer  becomes  a wattmeter  indicating  E I cos  (p 
when  the  current  is  passed  through  one  coil  and  a current  pro- 
portional to  and  in  phase  with  the  e.  m.  f.  through  the  other. 

If  the  current  in  the  pressure  coil  be  in  quadrature  with  the 
e.  m.  f.  the  instrument  indicates  El  sin  <p , the  wattless  volt  am- 
peres. 

This  is  easily  done  with  a two-phase  system.  With  a single- 
phase system  it  is  necessary  to  place  a proper  condenser  or  induc- 
tive reactance  in  series  with  the  pressure  coil. 

“ Wattless  Wattmeter sP  Induction  Type  (3c).  DobrowolskVs 
Power  Factor  Indicator 1. — In  a fully  compensated  induction 
meter  the  shunt  flux  is  in  quadrature  with  the  series  flux,  the 
result  of  the  two  being  a rotating  or  shifting  field.  If  the  shunt 
flux  be  brought  into  phase  with  the  series  flux  an  alternating  field 
only  will  be  set  up  as  long  as  the  current  and  e.  m.  f.  are  in  phase. 
If,  however,  the  current  lags,  the  field  will  rotate  in  one  direc- 
tion. If  it  leads,  the  field  will  rotate  in  the  opposite  direction. 
The  torque  developed  on  a disk  placed  in  this  field  is,  in  either 
case  proportional  to  El  sin  <p , the  wattless  volt  amperes.  This  is 
the  principle  of  Dobrowolski’s  apparatus. 

The  movable  disk  is  held  in  its  zero  position  by  a spring  when 
the  wattless  volt  amperes  are  zero,  but  deflects  one  way  or  the 
other,  when  the  current  is  out  of  phase,  an  amount  proportional 
to  El  sin  (p. 

Any  induction  wattmeter  can  be  used  in  this  way  provided  the 
flux  through  the  pressure  coil  be  brought  into  phase  with  the 

E.  M.  F. 


1.  U.  S.  latent  No.  549,449,  1896. 


1901.] 


BRO  WNE  ON  POWER  EAR  TOR  INDICATORS. 


489 


Wattless  Current  Meters  (4). — The  Allegemeine  Electricitats 
Gesellschaft  make  an  instrument1  which  indicates  the  wattless 
current.  This  is  really  an  induction  wattmeter  having  the  shunt 
flux  in  phase  with  the  e.  m.  f.  and  indicates  therefore  only  when 
there  is  a phase  difference.  As  an  instrument  of  this  type  indi- 
cates El  sin  <p , it  is  presumed  that  this  meter  is  graduated  to  read 


200 


600 


800 


I sin  (p  at  normal  voltage,  and  should  properly  come  under 
“ wattless  wattmeters”  (3c.) 

Behavior  of  Power  Factor  Indicators. 

The  Siemens  Electro-dynamometer.  = Th.Q  following  set  of 
curves  (Fig.  6)  were  taken  with  a Siemens  dynamometer,  the 


1.  L'  Eclairage  Electrique,  vol.  35,  p.  389. 


490 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


movable  coil  of  which  was  in  series  with  a capacity  of  3.5  micro- 
farads. The  values  of  cos  <p,  sin  <p  and  El  sin  y plotted  have  been 
computed  from  ammeter,  voltmeter  and  wattmeter  readings  given 
in  Table  I. 

El  sin  (p  is  a straight  line  and  is  plotted  above  and  below  the 
axis  todndicate  lagging  and  leading  currents  respectively.  The 
base^is  the  deflection  in  degrees.  These  curves  were  taken  for  a 
constant  power  delivered,  of  500  true  watts.  The  displacement 
of  current  was  obtained  by  means  of  a phasing  transformer.  For 
comparison  between  El  sin  <p  and  cos  <p  the  axis  of  .abscissae  is 
taken  as^unity  for  the  latter,  and  the  decreasing  values  plotted 
above  and  below  this. 


TABLE.  1. 

Siemens  Dynamometer  as  Power  Factor  Indicator. 


Amp. 

/ 

Volts 

E 

Watts 
El  cos  (j) 

Deflec- 

tion. 

Direc- 

tion. 

Phase 

Apparent 

watts 

El 

Power  fac- 
tors 
COS  <t> 

Induct- 
ance fact- 
ors sin  0 

AYsinc 

10.15 

108 

500 

213 

Right 

Lead 

1096 

• 456 

.889 

975 

8.4 

108 

500 

158 

“ 

907 

• 552 

• 834 

755 

7-58 

107.9 

500 

141 

“ 

*■ 

818 

.611 

.791 

647 

6.51 

108 

500 

106 

“ 

“ 

703 

.711 

•703 

494 

5-63 

107.8 

500 

78 

“ 

“ 

607 

.823 

.568 

294 

5-25 

107.8 

500 

53 

“ 

“ 

516 

.884 

.467 

241 

4.78 

105.5 

500 

13 

Left 

Lag 

504 

.992 

.126 

63 

5.05 

105.7 

500 

44 

“ 

“ 

533 

•938 

•346 

185 

5-67 

106. 1 

500 

76 

“ 

“ 

602 

.831 

•555 

334 

8.17 

106 

500 

155 

“ 

11 

866 

•577 

.817 

707 

9.61 

105.9 

500 

197 

U 

1007 

•497 

.867 

873 

Note. — Pressure  coil  in  series  with  3.5  microfarads  capacity. 


We  notice  first  that  these  lines  do  not  pass  through  the  origin. 
The  resistance  of  the  pressure  coil  is  not  negligible,  as  the  in- 
strument shows  a slight  deflection  at  unity  power  factor.  The 
curves  show  verjr  clearly  that  a slight  change  in  the  power  factor 
when  near  unity  caused  a comparatively  large  change  in  the 
value  of  El  sin  <p. 

This  fact  is  very  striking  when  working  with  the  instrument. 
It  may  be  made  to  deflect  considerably  to  the  right  or  left  with- 
out producing  any  appreciable  change  in  the  reading  of  the 
Weston  wattmeter,  the  current  and  voltage  remaining  constant 
the  while. 


1901.] 


BROWNE  ON  POWER  FAC 'LOR  INDICATORS. 


491 


Power  factors  for  larger  power  delivered,  lie  below  the  one 
just  considered  and  hence  are  still  flatter  when  approaching 
unity.  One  for  1,000  true  watts  has  been  plotted  from  calculated 
values  only.  It  shows  that  it  would  be  practically  impossible  to 
say  from  ammeter,  voltmeter  and  wattmeter  readings  alone, 
when  the  current  was  in  phase  with  the  e.  m.  f.  With  the  power 
factor  indicator,  however,  there  would  be  no  difficulty  in  getting 
an  almost  exact  adjustment. 


Fig.  7. 


f"  Weston  Wattmeter  as  Power  Factor  Indicator . — In  Fig.  7 is 
given  the  characteristic  of  a Weston  wattmeter  of  150  volts,  50 
amperes  capacity,  used  on  a two-phase  system  in  the  manner 
described  above.  The  characteristic  is  a straight  line,  but  does 
not  pass  through  the  origin. 

This  may  be  due  either  to  the  slight  inductance  of  the  pressure 
coil,  or  to  a slight  change  in  the  phase  angle  between  the  im- 
pressed e.  m.  f.’s  or  to  both. 


492 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


The  method  of  calibrating  consisted  in  connecting  the  pressure 
coils  of  the  power  factor  indicator  and  wattmeter  respectively  to 
the  two  primary  windings  of  a two-phase  induction  motor,  used 
as  a phasing  transformer.  The  current  coils  of  the  meters  were  in 
series  and  connected  to  the  movable  secondary.  As  the  secondary 
is  shifted,  the  load  is  partially  shifted  from  one  phase  of  the  primary 
winding  to  the  other.  This  doubtless  caused  a slight  change  in  the 
phase  angle  between  the  e.  m.  f.’s  at  the  motor  terminals.  The 
motor  used  was  rated  at  two  horse-power.  The  supply  was  drawn 
from  two  4 k.  w.  transformers,  both  partially  loaded  in  addition 
with  lights. 


TABLE  II. 

Weston  Wattmeters  as  Power  Factor  Indicator. 


True 

Watts. 

Vcltage. 

Amperes. 

Wattless 
volt  am- 
peres ob- 
served. 

Phase 

relation. 

Volt-am- 

peres. 

Power 

factor. 

Induct- 
ance fac- 
tor com- 
puted. 

Wattless 
volt-am- 
peres com- 
puted. 

IQ70 

in. 5 

44.4 

4530 

Lag 

4950 

•398 

. -9^7 

4540 

“ 

34 -7 

3325 

‘ 

387«>  ■ 

.509 

.860 

3330 

“ 

29.8 

2690 

334° 

.590 

.807 

2690 

“ 

25.0 

1950 

“ 

2790 

.706 

.708 

z975 

“ 

20.1 

1050 

“ 

2240 

.879 

•477 

1070 

“ 

17.7 

180 

“ 

1975 

•997 

.071 

140 

“ 

17.65 

0 

- 

1970 

1.0 

.0 

0 

20.1 

1130 

Lead 

2240 

.879 

•477 

1070 

25.0 

2050 

“ 

2790 

.706 

.708 

x975 

29.8 

2785 

“ 

3340 

•590 

.807 

269  1 

“ 

34-7 

3420 

“ 

3870 

•509 

.860 

333° 

44 

“ 

44.4 

461c 

“ 

4950 

•398 

.917 

454° 

The  agreement  between  observed  and  calculated  values  of  El 
sin  <p  is  good.  Table  II  gives  observed  and  computed  values  for 
this  instrument. 

Induction  Meters. — In  Fig.  8 are  shown  a set  of  curves  ob- 
tained from  a Shallenberger  integrating  wattmeter  used  as  a power 
factor  indicator.  The  instrument  is  a 500-volt,  10-ampere  meter 
of  the  older  type  (1898).  The  reactive  coil  was  replaced  by  a 
non-inductive  resistance  of  2, 000  ohms.  In  series  with  this  was  a 
capacity  of  3 mf.,  this  being  found  to  balance  the  inductance  of 
the  shunt  coil  at  a frequency  of  60  cycles.  In  this  case  the  in- 
strument was  used  as  a recording  meter.  The  curves  plotted  are  {} 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


493 


AT  sin  (p,  cos  <p  and  <p,  all  on  a revolutions  per  minute  base,  for  a 
delivered  power  of  500  true  watts.  Table  III  gives  the  instru- 
mental readings  and  computed  values  for  these  curves. 

Fig.  9 shows  the  results  from  the  same  meter  under  somewhat 
different  conditions.  Here  the  recording  train  was  removed  to 
lessen  the  friction,  and  a light  steel  spring  attached  to  the 
spindle  of  the  revolving  disk.  A pointer  attached  to  the  disk 


CD 


Fig.  8. 


-e- 

z 

co 

LU 

0 

300 

400 


800 

1000 


passed  over  a scale  marked  in  degrees.  The  curves  plotted  are, 
as  before,  El  sin  y>,  cos  <p  and  cp,  for  a delivered  power  of  500 
true  watts.  The  base  is  degrees  deflection.  It  will  be  noticed 
that  from  20°  lag  to  20°  lead  the  deflection  is  almost  directly 
proportional  to  the  phase  angle.  The  flattening  of  the  curve  for 
cos  <p  is  very  marked.  This  instrument  was  even  more  sensitive 
than  the  dynamometer  and  besides  was  dead  beat,  as  the  damping 


4 


494  BRO  WNE  ON  BO  WER  FACTOR  1NDICA10RS.  [Aug.  21, 

magnets  were  left  in.  Table  IY  gives  tlie  instrumental  readings 
and  computed  values  for  these  curves. 

Application  of  Power  Factor  Indicator. — To  illustrate  the 
application  of  a power  factor  indicator,  the  Weston  wattmeter 
mentioned  above  was  used  to  measure  the  wattless  volt  amperes 
taken  by  a General  Electric  7^-kilowatt,  125-volt,  four-pole, 
synchronous  converter  for  different  values  of  field  current.  The 
converter  was  run  on  a two-phase  system  at  constant  input.  The 
supply  was  drawn  from  two  Westinghouse  7-J-kilowatt  trans- 
formers, o.  d.  type,  fitted  with  a Hartford  regulator.  The 


TABLE  III. 

Shallenberger  Wattmeter  as  Power  Factor  Indicator.  10  amp.  400  volts. 


No. 

Amp. 

Volts. 

Watts 

r.p.m. 

Direc- 

tion. 

1 

Phase. 

Appar- 

ent 

watts 

El 

Power 
factor 
COS  (j) 

Phase 

Angle 

<p. 

Induct- 
ance fac- 
tor 

sin  <j> 

E /sin  (p 

1 

10. 01 

111.3 

505 

30.8 

Left 

Lagging 

1114 

•449 

63°  — io' 

.898 

996 

2 

8 

hi. 5 

5°5 

23-4 

“ 

“ 

891 

•567 

55—27 

.824 

734 

3 

6 

hi. 5 

505 

13-45 

“ 

“ 

669 

•756 

4o—53 

.655 

438 

4 

5-°7 

iri.o 

5°5 

7-45 

“ 

“ 

563 

.898 

26-^06 

.440 

248 

5 

4.78 

1 10. 3 

5°S 

4.68 

“ 

“ 

527 

•954 

17 — 26 

.300 

158 

6 

4-5 

hi. 9 

5°5 

0 

— 

- 

5°4 

1. 00 

0 

0 

0 

7 

4-58 

”4-5 

505 

5-29 

Right 

Leading 

525 

.962 

15—50 

•273 

M3 

8 

S-oo 

II4-3 

5°4 

8.7 

4- 

“ 

572 

.881 

28 — 14 

•473 

270 

9 

6.09 

112. 2 

5°5 

14.6 

“ 

“ 

684 

•738 

42 — 26 

•675 

462 

10 

8.0 

hi. 3 

5°5 

22.8 

“ 

“ 

890 

•567 

55-  28 

.824 

733 

11 

10. 0 

nr. 2 

505 

30.6 

“ 

1112 

•454 

63— CO 

.891 

992 

Note. — Impedance  coil  cut  out  and  shunt  coil  in  series  with  three  microfarads  and  2,000  ohms. 


output  was  absorbed  by  a lamp  bank  and  water  rheostat. 

In  Fig.  10,  armature,  current  and  wattless  volt  amperes  have 
been  plotted  as  ordinates,  the  base  being  field  current.  The  input 
was  3J  k.  w.  per  phase.  The  flatness  of  the  current  curve  alluded 
to  above  is  quite  noticeable  here.  The  characteristic  for  wattless 
volt  amperes  is  plotted  above  and  below  the  axis  of  abscissae  to 
indicate  lagging  and  leading  currents  respectively. 

The  instruments  were  quite  steady,  a condition  indicating  but 
little  hunting  of  the  armature,  although  there  were  no  devices  on 
the  machine  to  prevent  this  phenomenon.  The  power  factor  in- 
dicator, although  exactly  like  the  wattmeter,  was  even  steadier 
than  the  latter.  There  was  no  difficulty  in  setting  the  indicator 
to  read  any  desired  value  by  adjusting  the  field  current. 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


495 


It  was  stated’  at  a recent  meeting  of  the  National  Electric 
Light  Association,  during  the  discussion  of  a paper  on  synchronous 
converters,  that  it  was  practically  impossible  to  operate  a syn- 
chronous motor  or  converter  at  unity  power  factor.  The  reasons 
given  were  hunting  of  the  armature  and  dissimilar  e.  m.  f.  waves 
of  motor  and  generator.  In  the  above  experiment  it  was  found 
that  the  power  factor  indicator  could  be  set  at  zero  and  under 
these  conditions  the  true  watts  and  the  volt  amperes  were  equal. 
This  condition  would  seem  to  be  that  of  practically  unity  power 
factor. 


800 

TOO 

600 

500 

400 

300 

200 

.100 

0 

o 

5 

.■©• 

z 

CO 

HH 

LxJ 


Fig.  9. 

A number  of  power  factor  curves  of  synchronous  converters 
have  been  published  recently  in  which  the  current  passes  from 
lag  to  lead  without  the  power  factor  passing  through  unity.  Even 
if  it  were  impossible  to  hold  the  power  factor  at  unity,  it  must 
pass  through  this  value  as  it  swings  across  the  line. 

In  Fig.  11  are  plotted,  on  an  excitation  base,  curves  of  power 
factor  from  wattmeter  readings  and  inductance  factor  from  the 


1.  Western  Electrician , Feb.  9,  1901. 


496  BRO  WNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 

“wattless  wattmeter”  readings.  In  addition  there  have  been 
plotted  two  curves  obtained  by  assuming  these  values  to  be  cosines 
and  ^ines  of  phase  angles  and  the  corresponding  values  of  sines 
and  cosines  taken  from  tables  and  plotted  on  the  same  base. 
These  deduced  values  do  not  agree  at  all  with  the  observed  ones. 
The  discrepancy  is  greater  for  leading  than  lagging  currents. 
This  discrepancy,  as  has  been  pointed  out  by  Mr.  Steinmetz1,  is: 


TABLE  IV. 

Shallenberger  Wattmeter  as  Power  Factor  Indicator. 


No. 

Amp- 

eres. 

Volts. 

True 

watts. 

Degrees 

deflection. 

Direc- 

tion. 

Phase 

Apparent 

watts. 

COS  (p 

0 

sin  0 

El  sin  (j> 

i 

8.29 

no. 

500 

75° 

Left 

Lag. 

911 

•549 

560— 42' 

.836 

761 

2 

7.27 

108.5 

500 

60 

“ 

788 

•634 

50—39 

•773 

608 

3 

6.54 

icg. 

500 

50 

“ 

712 

.702 

45—35 

.712 

507 

4 

5-85 

110.5 

500 

40 

“ 

646 

• 774 

39—17 

•633 

409 

5 

5-41 

109.2 

500 

30 

“ 

590 

.848 

32 — 00 

•530 

3*3 

6 

4.94 

109.9 

500 

20 

“ 

543 

.921 

22 — 56 

•39° 

212 

7 

4-57 

nr. 1 

500 

IC 

“ 

507 

.987 

9—04 

.158 

80 

8 

4-59 

108.4 

500 

0 

- 

- 

498 

1. 

0 

0 

0 

9 

4-67 

109. 

500 

10 

Right 

Lead 

509 

.982 

10—53 

.189 

96 

IO 

5-35 

108. 

500 

30 

“ 

“ 

578 

.865 

30—07 

.502 

290 

1 1 

5-87 

109.4 

500 

40 

“ 

“ 

642 

.78 

38—44 

.626 

402 

12 

6-45 

109.7 

500 

50 

“ 

“ 

707 

.708 

45—05 

.706 

498 

13 

7-44 

107.4 

500 

60 

*• 

799 

.626 

5i—i3 

•779 

623 

i4 

8.16 

108.7 

500 

70 

“ 

886 

•564 

55—40 

.826 

732 

Note.— Impedance  coil  removed  and  shunt  coil  in  series  with  three  microfarads  and  2,000  ohms 
non-inductive  resistance.  Recording  gear  removed  and  light  torsion  spring  attached  to  disk. 


due  to  the  distortion  of  the  e.  m.  f.  and  current  waves. 

Table  Y gives  observed  and  computed  values  for  these 
curves. 

Conclusions.— It  would  seem  from  the  above  that  there  is  a 
decided  need  of  an  accurate  power  factor  indicator  in  all  large 
installations,  but  especially  in  those  in  which  induction  and  syn- 
chronous motors  are  used  together.  This  method  of  operation 
has  been  adopted  by  the  Deering  Harvester  Company,  where  ad- 
justment of  the  exciting  current  of  the  synchronous  machine  is 


1.  Symbolic  Representation  of  General  Alternating  Waves  and  of  Double- 

Frequency  Products.  C.  P.  Steinmetz,  Transactions,  vol.  16,  p.  289,  1899. 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


497 


made  by  means  of  a wattmeter,  and  at  Butte,  Montana1,  where 
adjustment  is  made  from  ammeter  readings.  The  advisability  of 
adopting  this  composite  system  is  not  in  question  here.  We  are 
considering  merely  the  best  method  of  attaining  the  end  sought. 


70 

7000 

Ij 

60 

6000 

V 

50 

o 

5000  § 

Il\  ' 

CO 

40  £ 

_j 

h 

4000  < 

S 

AMP 

CO 

1x1 

3000  t 

20 

$ 

2000 

10 

1000 

0 

0 o 

5 

1 

0 

\l 

5 

2 

,0 

2 

5 

3 

1000 

AMPERES 

EXCITA1 

ION 

2000 

3000 

LEADING 

\o 

5000 

6000 

GENERAL  ELECTRIC  SYNCHRONOUS  CONVERTER 
7-K  KW.  125  V.  4 POLE,  60  A/ 

I- I  ARMATURE  CURRENT 

II- II  “WATTLESS  WATTS” 

7000 

n 

Fig.  10. 


For  accurate  adjusting  of  the  system  the  indications  of  the  in- 
strument should  depend  upon  the  values  of  <p  or  sin  <p  and  not 
upon  cos  (p. 

Instruments  of  the  dynamometer  or  the  induction  type  seem 
more  suitable  for  operating  conditions.  If  the  meter  be  of  the 

1.  Elec.  Lt.  & Power  at  Butte,  Mont.  J.  R.  Cravath,  Elec.  W.  & E.,  vol 
37,  p.  149,  Jan.  26,  1901. 


498 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


dynamometer  type  the  resistance  of  the  pressure  coil  must  be 
negligible  if  it  is  to  be  used  on  a single-phase  system,  as  the  cur- 


o 

< 

-J 

o 

0.9  5 

-SF 

CO 

O 

o 

■€P 

0.8  g 

'GENERAL  ELECTRIC  SYNCHRONOUS  CONVERTER 
1-Yz  KW.  125  V.  4 POLE  60  A J 

T-I  POWER  FACTOR,  OBSERVED 

II- II  INDUCTANCE  FACTOR,  “ 

III- III  SIN  0 FROM  CURVE  I 

IV- IV  COS  0 FROM  CURVE  II 

ce 

O 

o 

< 

u. 

o 

< 

0.7  o 

5 

o 

CL 

0.4 

< 

0.6 1 

0.5 

0.5  > 

0.6 

0.4 

\ 

0.7 

0.3 

0.8 

0.2 

0.9 

0.1 

• 

1.0 

0 0 

5 

1 

,0 

o\ 

.5 

2 

,0 

2 

5 

3 

0.9 

0.1 

AMPERES 

EXCIT/ 

mON 

0.8 

0.2 

\ ° 

0.7 

0.3 

\ o 

0.6 

0.4 

0.5 

0.5 

0.4 

0.6 

r\\ 

0.3 

0.7 

o \ 

\ + 

0.8 

• 

/s 

LEAD 

P 1 

° leadI 

1.0 

Fig.  11. 

rent  in  this  coil  must  be  in  quadrature  with  the  e.  m.  f. 

If  the  meter  is  to  be  used  on  a two  or  a three-phase  system, 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


499 


the  inductance  of  the  pressure  coil  must  be  negligibly  small,  and 
meter  connected  in  one  of  the  methods  described  above.  In  this 
case  care  must  be  taken  that  the  loads  on  the  different  phases  be 
kept  equal.  In  a two-phase  system,  unbalancing  the  phases  will 
shift  the  e.  m.  f.’s  relatively  to  each  other.  In  a three-phase  sys- 
tem, since  the  meters  used  are  really  wattmeters,  unbalancing  the 
phases  will  vitiate  the  indications  of  the  instrument. 

If  the  meter  be  of  the  induction  type  the  inductance  of  the 
pressure  coil  must  be  negligible,  since  not  only  is  it  undesirable 

TABLE  V. 


General  Electric  Synchronous  Converter.  7-^k.w.,  125  v.,  4-pole,  60  2-phase. 
Input  3.5  k.w.  per  phase. 


Wattless 
kilo- volt 
amperes. 

Amperes 

armature 

current. 

Voltage 

at 

brushes. 

Amp- 

eresfield 

current. 

Phase 

relation. 

Kilovolt 

amperes 

Power 

factor. 

Induc- 

tance 

factor. 

sin  <j> 

computed 
from  pow- 
er factor. 

COS  (p 
computed 
from  in- 
ductance 
factor. 

5-55 

6t.6 

109.9 

0.57 

Lag 

6 76 

.518 

822 

•855 

.569 

4-23 

51*3 

1 10.0 

O 

00 

5-64 

.621 

•750 

•784 

.661 

2.62 

40.9 

109.9 

r.03 

“ 

4-5 

.778 

■583 

.628 

.812 

1 45 

35  7 

109.7 

1.2 

“ 

3 91 

.895 

•37i 

.446 

.929 

o-45 

32  0 

109.8 

1.36 

“ 

3-5i 

•997 

.128 

.077 

.992 

— 0.05 

3*-9 

109.8 

1.47 

Lead 

3-5° 

1.0 

.014 

.0 

•999 

— o-45 

32.1 

1 ie.o 

r.55 

“ 

3-53 

992 

.128 

.126 

.992 

— 1.20 

35-7 

no. 4 

1.69 

“ 

3-94 

.888 

.306 

.460 

•952 

— 2.22 

40.9 

O 

bo 

1.88 

“ 

4-49 

•779 

•495 

.627 

.869 

— 365 

5i-3 

IIO.O 

2.22 

“ 

5-64 

.621 

.648 

.784 

.762 

— 5 3° 

6r.6 

IIO. 2 

2.5 

“ 

6.78 

.516 

.782 

•857 

.623 

— 6 65 

71.9 

■ 0&8 

••75 

“ 

7 89 

•444 

• 844 

.896 

.536 

to  use  condensers  to  compensate  for  this,  both  from  their  bulki- 
ness and  expense,  but  the  presence  of  any  reactance  makes  the 
deflection  dependent  upon  the  frequency.  An  attempt  was  made 
to  improve  upon  the  induction  meter  described  above  by  remov- 
ing the  three-legged  stampings  of  iron  upon  which  the  pressure 
coil  was  wound.  The  inductance  was  still  too  large  for  satisfac- 
tory working  and  as  the  condensers  in  the  laboratory  were  not 
sufficient  to  compensate  for  this,  it  was  necessary,  to  make  up 
for  this  lack  of  capacity  and  to  avoid  the  use  of  iron,  to  add  an 
auxiliary  inductance  wound  on  a wooden  bobbin.  The  instru- 
ment thus  modified  was  found  to  be  so  sensitive  to  slight  changes 
in  frequency  that  it  was  impossible  to  use  it  with  any  degree  of 


600 


BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22, 


satisfaction  in  the  laboratory.  Any  change  of  load  on  the  prime 
mover  would  so  change  the  reading  of  the  instrument  as  to  make 
its  indications  extremely  unreliable. 

Dobrowolski  shows,  in  the  reference  given  above,  the  applica- 
tion of  his  instrument  for  automatically  adjusting  the  excitation 
of  the  synchronous  machine  so  as  to  keep  the  power  factor  at 
unity  at  all  times. 

The  use  of  an  instrument  of  this  kind  emphasizes  the  fact  that, 
when  induction  motors  are  used  alone,  the  inductance  factor  is 
always  a large  percentage  of  the  power  factor.  For  instance, 
when  the  power  factor  is  .85  the  inductance  factor,  assuming 
sinusoidal  waves,  is  nearly  62%  of  this.  That  is,  for  every  kilo- 
watt used  by  the  motor,  620  c£  wattless  watts  ” are,  so  to  speak, 
borrowed.  It  would  seem  but  fair  that  those  who  use  induction 
motors  should  at  least  pay  rental  for  the  wattless  volt  amperes 
required.  It  is  true  this  does  not  represent  energy  consumed, 
but  it  does,  in  a sense,  represent  energy  borrowed  and  returned 
and  the  station  must  have  sufficient  capacity  in  generators  to 
meet  all  such  calls  for  loans. 

The  additional  charge  could  be  taken  care  of  by  over-com- 
pensating integrating  wattmeters  of  the  induction  type,  as  sug- 
gested by  Mr.  Benischke.  They  would  then  read  high  on  lagging 
reactive  loads  and  low  on  leading  reactive  loads.  This  would  put 
a premium  on  the  use  of  synchronous  motors  as  they,  if  not  too 
greatly  over-excited,  help  out  in  the  regulation  of  the  plant.  The 
induction  motor  has  so  many  points  in  its  favor  it  can  well 
afford  to  pay  for  what  it  needs— a large  wattless  component  of 
current. 


1901.] 


BROWNE  ON  POWER  FACTOR  INDICATORS. 


499 


the  inductance  of  the  pressure  coil  must  be  negligibly  small,  and 
meter  connected  in  one  of  the  methods  described  above.  In  this 
case  care  must  be  taken  that  the  loads  on  the  different  phases  be 
kept  equal.  In  a two-phase  system,  unbalancing  the  phases  will 
shift  the  e.  m.  f.’s  relatively  to  each  other.  In  a three-phase  sys- 
tem, since  the  meters  used  are  really  wattmeters,  unbalancing  the 
phases  will  vitiate  the  indications  of  the  instrument. 

If  the  meter  be  of  the  induction  type  the  inductance  of  the 
pressure  coil  must  be  negligible,  since  not  only  is  it  undesirable 

TABLE  V. 


General  Electric  Synchronous  Converter.  7-Jk.w.,  125  v.,  4-pole,  60  2- phase. 

Input  3.5  k.w.  per  phase. 


Wattless 
kilo- volt 
amperes. 

Amperes 

armature 

current. 

Voltage 

at 

brushes. 

Amp- 
eres field 
current. 

Phase 

relation. 

Kilovolt 

amperes 

Power 

factor. 

Induc- 

tance 

factor. 

sin  (j) 

computed 
from  pow- 
er factor. 

COS  (p 
computed 
from  in- 
ductance 
factor. 

5-55 

6t.6 

109.9 

o-57 

Lag 

6 76 

.518 

822 

•855 

•569 

4-23 

5T-3 

I 10.0 

0.78 

5-64 

.621 

• 75° 

.784 

.661 

2.62 

40.9 

109.9 

1.03 

“ 

4-5 

.778 

•583 

.628 

.8x2 

1 45 

35  7 

109  7 

1.2 

“ 

3 91 

.895 

•37i 

.446 

.929 

0-45 

32  0 

109.8 

T.36 

“ 

3-5i 

•997 

.128 

.077 

.992 

— 0.05 

3i-9 

icg.8 

I.47 

Lead 

3-5° 

1.0 

.014 

.0 

•999 

— o-45 

32.1 

I IC.O 

t-55 

“ 

3-53 

992 

.128 

.126 

.992 

— 1.20 

35-7 

1 10.4 

I.69 

“ 

3-94 

.888 

.306 

.460 

•952 

— 2.22 

40.9 

109.8 

1.88 

“ 

4-49 

•779 

•495 

.627 

.869 

— 3 65 

5t-3 

rio.o 

2.22 

“ 

5-64 

.621 

.648 

.784 

.762 

— 5 30 

6r.6 

no. 2 

2.5 

6.78 

• 5*6 

.782 

•857 

.623 

— 6 65 

71.9 

io  >.8 

-•75 

“ 

7 89 

•444 

.844 

.896 

•536 

to  use  condensers  to  compensate  for  this,  both  from  their  bulki- 
ness and  expense,  but  the  presence  of  any  reactance  makes  the 
deflection  dependent  upon  the  frequency.  An  attempt  was  made 
to  improve  upon  the  induction  meter  described  above  by  remov- 
ing the  three-legged  stampings  of  iron  upon  which  the  pressure 
coil  was  wound.  The  inductance  was  still  too  large  for  satisfac- 
tory working  and  as  the  condensers  in  the  laboratory  were  not 
sufficient  to  compensate  for  this,  it  was  necessary,  to  make  up 
for  this  lack  of  capacity  and  to  avoid  the  use  of  iron,  to  add  an 
auxiliary  inductance  wound  on  a wooden  bobbin.  The  instru- 
ment thus  modified  was  found  to  be  so  sensitive  to  slight  changes 
in  frequency  that  it  was  impossible  to  use  it  with  any  degree  of 


600  BROWNE  ON  POWER  FACTOR  INDICATORS.  [Aug.  22 

satisfaction  in  the  laboratory.  Any  change  of  load  on  the  prime 
mover  would  so  change  the  reading  of  the  instrument  as  to  make 
its  indications  extremely  unreliable. 

Dobrowolski  shows,  in  the  reference  given  above,  the  applica- 
tion of  his  instrument  for  automatically  adjusting  the  excitation 
of  the  synchronous  machine  so  as  to  keep  the  power  factor  at 
unity  at  all  times. 

The  use  of  an  instrument  of  this  kind  emphasizes  the  fact  that, 
when  induction  motors  are  used  alone,  the  inductance  factor  is 
always  a large  percentage  of  the  power  factor.  For  instance, 
when  the  power  factor  is  .85  the  inductance  factor,  assuming 
sinusoidal  waves,  is  nearly  62%  of  this.  That  is,  for  every  kilo- 
watt used  by  the  motor,  620  “ wattless  watts  ” are,  so  to  speak, 
borrowed.  It  would  seem  but  fair  that  those  who  use  induction 
motors  should  at  least  pay  rental  for  the  wattless  volt  amperes 
required.  It  is  true  this  does  not  represent  energy  consumed, 
but  it  does,  in  a sense,  represent  energy  borrowed  and  returned 
and  the  station  must  have  sufficient  capacity  in  generators  to 
meet  all  such  calls  for  loans. 

The  additional  charge  could  be  taken  care  of  by  over-com- 
pensating integrating  wattmeters  of  the  induction  type,  as  sug- 
gested by  Mr.  Benischke.  They  would  then  read  high  on  lagging 
reactive  loads  and  low  on  leading  reactive  loads.  This  would  put 
a premium  on  the  use  of  synchronous  motors  as  they,  if  not  too 
greatly  over-excited,  help  out  in  the  regulation  of  the  plant.  The 
induction  motor  has  so  many  points  in  its  favor  it  can  well 
afford  to  pay  for  what  it  needs — a large  wattless  component  of 
current. 


